Finite Group Databasebeta

← #14307138

Subgroups — #14307138

Order 1920.

520 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754615C211yesmaximal, characteristic
2C3×C4×#683C211yesmaximal, characteristic
3Dic5×#208C211yesmaximal, characteristic
4#11746344C211yesmaximal, characteristic
5C5×#4523C211yesmaximal, characteristic
6#11745978C211yesmaximal, characteristic
7#11745977C211yesmaximal, characteristic
8#10599523—31nomaximal, Hall
9C2×C3×C42×C5C2211yescharacteristic
10#91815C2211yescharacteristic
11C2×#6710C2211yescharacteristic
12C5×#926C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C2×C3×#683—21no—
15C2×C3×C4×Dic5C2211yescharacteristic
16C2×C3×C4×Dic5C2211yescharacteristic
17#91574—21no—
18#91574—21no—
19#91468C411yescharacteristic, complemented
20#91468C411yescharacteristic, complemented
21C4×#1204—21no—
22C4×#1204—21no—
23#91388C411yescharacteristic, complemented
24#91388C411yescharacteristic, complemented
25C3×#3963—21no—
26#90952—21no—
27Dic5×C3⋊C8—21no—
28#69493—51nomaximal, Hall
29#65851—31no—
30M16×Dic5—31no—
31C4×#683D311yescharacteristic
32C5×#339—31no—
33#64775—31no—
34#64752—31no—
35#64743—31no—
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C22×C3×Dic5—21no—
39C22×C3×Dic5D411yescharacteristic
40C22×C3×Dic5D411yescharacteristic
41C2×#1204—21no—
42C2×#1204—21no—
43C3×C42×C5—21no—
44C3×C42×C5—21no—
45#6719—21no—
46C4⋊Dic15C2×C411yescharacteristic
47C4⋊Dic15C2×C411yescharacteristic
48C4×Dic15—21no—
49#6710—21no—
50#6710Q812yescomplemented
51C2×C3⋊#168—21no—
52C5×#217—21no—
53C5×C4⋊Dic3C2×C411yescharacteristic
54C5×C4⋊Dic3C2×C411yescharacteristic
55C4×C5×Dic3—21no—
56C5×#208—21no—
57C5×#208Q812yescomplemented
58C2×C5×C3⋊C8—21no—
59C3×#683—24no—
60C3×C4×Dic5—21no—
61C3×C4×Dic5—21no—
62C3×C4×Dic5C2×C411yescharacteristic
63C3×C4×Dic5C2×C411yescharacteristic
64C3×C4×Dic5D411yescharacteristic
65C3×C4×Dic5D411yescharacteristic
66Dic3⋊Dic5—21no—
67Dic3⋊Dic5—21no—
68#6669—21no—
69#6669—21no—
70#6668—21no—
71#6668—21no—
72#5470—51no—
73C3×C4×C4⋊C4—51no—
74C4×#208—51no—
75#4523—51no—
76#4523—51no—
77#4523—51no—
78#4523D511yescharacteristic
79C2×C5×M16—31no—
80C5×#117—31no—
81C2×C42×C5C2×D311yescharacteristic
82#4072—31no—
83C2×#683—21no—
84C2×C4×Dic5C2×D311yescharacteristic
85C2×C4×Dic5C2×D311yescharacteristic
86C2×#681—31no—
87#4036—31no—
88#4036—31no—
89#4034—31no—
90#4034—31no—
91#4024—61no—
92#4024—61no—
93C4×Dic10—61no—
94C4×Dic10—61no—
95#3963—21no—
96#3947—61no—
97C8×Dic5—61no—
98#1986—151noSylow
99C23×C3×C5C2×D411yescharacteristic
100C2×C3×C4×C5—22no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5C22×C411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×Q811yescharacteristic
106C2×C3×C4×C5C2×Q811yescharacteristic
107C2×C3×C4×C5#4111yescharacteristic
108C2×C3×C4×C5#4111yescharacteristic
109C2×Dic15—21no—
110C2×Dic15—21no—
111C2×C5×Dic3—21no—
112C2×C5×Dic3—21no—
113C2×C3×Dic5—22no—
114C2×C3×Dic5—22no—
115C2×C3×Dic5—41no—
116C2×C3×Dic5—41no—
117C2×C3×Dic5—41no—
118C2×C3×Dic5C22⋊C411yescharacteristic
119C2×C3×Dic5C22⋊C411yescharacteristic
120C2×C3×Dic5C22⋊C411yescharacteristic
121C2×C3×Dic5C22⋊C411yescharacteristic
122#1204—42no—
123#1204—42no—
124C3⋊#168—22no—
125C5×C3⋊C8—22no—
126C2×C3×C4⋊C4—101no—
127C2×C3×C42—51no—
128C2×C3×C42—51no—
129C2×C3×C42C2×D511yescharacteristic
130#926—51no—
131#926C2×D511yescharacteristic
132#924—101no—
133#924—101no—
134C2×#208—51no—
135C2×#208C2×D511yescharacteristic
136#870—51no—
137#870—51no—
138#869—51no—
139#869—51no—
140C4×Dic6—101no—
141C4×Dic6—101no—
142C3×#95—101no—
143#803—101no—
144C4×C3⋊C8—101no—
145C22×C4×C5—21no—
146C22×C4×C5C22×D311yescharacteristic
147C22×Dic5—21no—
148C22×Dic5#6711yescharacteristic
149C22×Dic5#6711yescharacteristic
150C2×Dic10—61no—
151C2×Dic10—61no—
152C5×M16—32no—
153C5×M16—61no—
154C2×C5×C8—61no—
155C5×C4⋊C4—31no—
156C5×C4⋊C4—31no—
157C5×C22⋊C4—61no—
158C42×C5—21no—
159C42×C5—21no—
160C42×C5—61no—
161C22⋊Dic5—61no—
162C4⋊Dic5—31no—
163C4⋊Dic5—31no—
164C4⋊Dic5—61no—
165C4⋊Dic5—61no—
166#683—24no—
167#683—61no—
168#683—61no—
169#683—61no—
170#683—61no—
171C4×Dic5—21no—
172C4×Dic5—21no—
173C4×Dic5—61no—
174C4×Dic5C4×D311yescharacteristic
175C4×Dic5C4×D311yescharacteristic
176C4×Dic5D1211yescharacteristic
177C4×Dic5D1211yescharacteristic
178#681—32no—
179#681—61no—
180C2×#168—61no—
181#533—151no—
182C4×M16—151no—
183C4×C4⋊C4—51no—
184#339—31no—
185#339—151no—
186#339—151no—
187#339—151no—
188C22×C3×C5—21no—
189C22×C3×C5—21no—
190C22×C3×C5C2×C22⋊C411yescharacteristic
191C22×C3×C5#12411yescharacteristic
192C22×C3×C5C4⋊Q811yescharacteristic
193C3×C4×C5—42no—
194C3×C4×C5C4×Q811yescharacteristic
195C3×C4×C5C4×Q811yescharacteristic
196C3×C4×C5C22⋊Q811yescharacteristic
197C3×C4×C5C22⋊Q811yescharacteristic
198Dic15—41no—
199Dic15—41no—
200C3×Dic5—21no—
201C3×Dic5—21no—
202C3×Dic5—21no—
203C3×Dic5—42no—
204C3×Dic5#10412yes—
205C5×Dic3—41no—
206C5×Dic3—41no—
207C22×C3×C4—21no—
208C22×C3×C4—51no—
209C22×C3×C4—51no—
210C22×C3×C4—101no—
211C22×C3×C4C22×D511yescharacteristic
212C2×Dic6—101no—
213C2×Dic6—101no—
214C3×C4⋊C4—104no—
215C3×C42—21no—
216C3×C42—21no—
217C3×C42—51no—
218C3×C42—51no—
219C3×C42—51no—
220C3×C42—51no—
221C3×C42—101no—
222C3×C42—101no—
223#217—21no—
224#217—101no—
225C4⋊Dic3—51no—
226C4⋊Dic3—51no—
227C4⋊Dic3—101no—
228C4⋊Dic3—101no—
229C4⋊Dic3C4×D511yescharacteristic
230C4⋊Dic3C4×D511yescharacteristic
231Dic3⋊C4—101no—
232Dic3⋊C4—101no—
233Dic3⋊C4—101no—
234Dic3⋊C4—101no—
235C4×Dic3—21no—
236C4×Dic3—101no—
237#208—21no—
238#208—52no—
239#208—101no—
240#208Dic1012yescomplemented
241C2×C3⋊C8—21no—
242C2×C3⋊C8—101no—
243C23×C5C2×#6711yescharacteristic
244C2×C4×C5—22no—
245C2×C4×C5—41no—
246C2×C4×C5—41no—
247C2×C4×C5—61no—
248C2×C4×C5—61no—
249C2×C4×C5C2×C4×D311yescharacteristic
250C2×C4×C5C2×D1211yescharacteristic
251C2×C4×C5#23711yescharacteristic
252C2×C4×C5#23711yescharacteristic
253C2×C4×C5D3×Q811yescharacteristic
254C2×C4×C5D3×Q811yescharacteristic
255C2×Dic5—22no—
256C2×Dic5—22no—
257C2×Dic5—41no—
258C2×Dic5—41no—
259C2×Dic5—41no—
260C2×Dic5—61no—
261C2×Dic5—61no—
262C2×Dic5(C2×D3)⋊C411yescharacteristic
263C2×Dic5(C2×D3)⋊C411yescharacteristic
264C2×Dic5(C2×D3)⋊C411yescharacteristic
265C2×Dic5(C2×D3)⋊C411yescharacteristic
266Dic10—122no—
267Dic10—122no—
268C5×C8—62no—
269#168—62no—
270C2×M16—31no—
271C2×M16—151no—
272C4⋊Q8—151no—
273C4⋊Q8—151no—
274#125—151no—
275#125—151no—
276C22⋊Q8—301no—
277C22⋊Q8—301no—
278C4×Q8—301no—
279C4×Q8—301no—
280#117—31no—
281#117—151no—
282C2×C4⋊C4—101no—
283C2×C42—51no—
284C2×C42—51no—
285C2×C42D3×D511yescharacteristic
286#97—301no—
287C4×C8—301no—
288#95—101no—
289C2×C3×C5—21no—
290C2×C3×C5—21no—
291C2×C3×C5#39111yescharacteristic
292C2×C3×C5C2×#10411yescharacteristic
293C2×C3×C5#42111yescharacteristic
294C23×C3D4×D511yescharacteristic
295C2×C3×C4—22no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—51no—
299C2×C3×C4—51no—
300C2×C3×C4—51no—
301C2×C3×C4—51no—
302C2×C3×C4—102no—
303C2×C3×C4—102no—
304C2×C3×C4—201no—
305C2×C3×C4—201no—
306C2×C3×C4—201no—
307C2×C3×C4C2×Dic1011yescharacteristic
308C2×C3×C4C2×C4×D511yescharacteristic
309C2×C3×C4#70911yescharacteristic
310C2×C3×C4D4×D511yescharacteristic
311C2×C3×C4#71111yescharacteristic
312C2×C3×C4Q8×D511yescharacteristic
313C2×Dic3—21no—
314C2×Dic3—21no—
315C2×Dic3—101no—
316C2×Dic3—101no—
317Dic6—202no—
318Dic6—202no—
319C3⋊C8—22no—
320C3⋊C8—102no—
321C22×C5—21no—
322C22×C5—21no—
323C22×C5C2×(C2×D3)⋊C411yescharacteristic
324C22×C5#93611yescharacteristic
325C22×C5#94411yescharacteristic
326C4×C5—42no—
327C4×C5—121no—
328C4×C5—121no—
329C4×C5#88711yescharacteristic
330C4×C5#88711yescharacteristic
331C4×C5#89711yescharacteristic
332C4×C5#89711yescharacteristic
333Dic5—21no—
334Dic5—21no—
335Dic5—21no—
336Dic5—42no—
337Dic5—121no—
338Dic5—121no—
339Dic5#80512yes—
340C2×Q8—301no—
341C2×Q8—301no—
342C22×C4—21no—
343C22×C4—51no—
344C22×C4—51no—
345C22×C4—101no—
346C22×C4C2×D3×D511yescharacteristic
347M16—32no—
348M16—61no—
349M16—152no—
350M16—301no—
351C2×C8—61no—
352C2×C8—301no—
353C4⋊C4—31no—
354C4⋊C4—31no—
355C4⋊C4—104no—
356C4⋊C4—151no—
357C4⋊C4—151no—
358C4⋊C4—301no—
359C4⋊C4—301no—
360C4⋊C4—301no—
361C4⋊C4—301no—
362C4⋊C4—301no—
363C4⋊C4—301no—
364C22⋊C4—61no—
365C22⋊C4—301no—
366C42—21no—
367C42—21no—
368C42—51no—
369C42—51no—
370C42—51no—
371C42—51no—
372C42—61no—
373C42—101no—
374C42—101no—
375C42—301no—
376C3×C5#198611yescharacteristic, complemented, Hall
377C22×C3—21no—
378C22×C3—21no—
379C22×C3D5×C22⋊C411yescharacteristic
380C22×C3#403111yescharacteristic
381C22×C3#403411yescharacteristic
382C3×C4—42no—
383C3×C4—52no—
384C3×C4—101no—
385C3×C4—101no—
386C3×C4—101no—
387C3×C4—202no—
388C3×C4C4×Dic1011yescharacteristic
389C3×C4#402411yescharacteristic
390C3×C4#403311yescharacteristic
391C3×C4#404211yescharacteristic
392Dic3—41no—
393Dic3—41no—
394Dic3—201no—
395Dic3—201no—
396C2×C5—21no—
397C2×C5—21no—
398C2×C5C2×#80511yescharacteristic
399C2×C5#497311yescharacteristic
400C2×C5#500511yescharacteristic
401C23D5×#6711yescharacteristic
402Q8—602no—
403Q8—602no—
404C2×C4—22no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—51no—
408C2×C4—51no—
409C2×C4—51no—
410C2×C4—51no—
411C2×C4—61no—
412C2×C4—61no—
413C2×C4—102no—
414C2×C4—102no—
415C2×C4—201no—
416C2×C4—201no—
417C2×C4—201no—
418C2×C4—301no—
419C2×C4—301no—
420C2×C4D3×Dic1011yescharacteristic
421C2×C4D15⋊Q811yescharacteristic
422C2×C4C4×D3×D511yescharacteristic
423C2×C4D5×D1211yescharacteristic
424C2×C4#677911yescharacteristic
425C2×C4#678011yescharacteristic
426C8—62no—
427C8—302no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3#6493511yescharacteristic
431C2×C3D5×#10411yescharacteristic
432C2×C3#6511011yescharacteristic
433C5#6949311yescharacteristic, complemented, Sylow
434C22—21no—
435C22—21no—
436C22#9132711yescharacteristic
437C22D5×(C2×D3)⋊C411yescharacteristic
438C22#9153411yescharacteristic
439C4—42no—
440C4—52no—
441C4—101no—
442C4—101no—
443C4—101no—
444C4—121no—
445C4—121no—
446C4—202no—
447C4—601no—
448C4—601no—
449C4#9132411yescharacteristic
450C4#9132511yescharacteristic
451C4#9141711yescharacteristic
452C4#9141911yescharacteristic
453C3#1059952311yescharacteristic, complemented, Sylow
454C2—21no—
455C2—21no—
456C2D5×#80511yescharacteristic
457C2#1174710911yescharacteristic
458C2#1174862811yescharacteristic
subgroupG/H
centerC2×C4D5×D12
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C2×D4
cosocleC22×C3×C4×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1986
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
19. #91468C4semidirect
20. #91468C4semidirect
23. #91388C4semidirect
24. #91388C4semidirect
50. #6710Q8semidirect
57. C5×#208Q8semidirect
240. #208Dic10semidirect
376. C3×C5#1986semidirect
433. C5#69493semidirect
453. C3#10599523semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#117546152
C3×C4×#6832
Dic5×#2082
#117463442
C5×#45232
#117459782
#117459772
#105995233
#694935